Asymptotics of the Eigenelements of the Laplace Operator when the Boundary-Condition Type Changes on a Narrow Flattened Strip

In this paper, the method of matching asymptotic expansions is used to construct an asymptotics (in a small parameter) of the eigenvalues and eigenfunctions of the Laplace operator in a domain when the boundary-condition type changes on a narrow flattened strip, provided that on the narrow strip of the boundary a Neumann condition is given and on the remaining part of the boundary a Dirichlet condition is given. The width of the strip is taken as the small parameter.